Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

138 THEORY OF PRODUCTION [CHAP. 6
6.16 Suppose that P K ¼ $1, P L ¼ $2, and TO ¼ $16. (a) What is the slope of the isocost? (b) Write the
equation for the isocost. (c) What do we means by P L ? P K ?
(a)
(b)
If we plot labor along the horizontal axis and capital along the vertical axis, the slope of the isocost is equal to
2P L /P K ¼ 22.
The equation of the straight-line isocost is given by
TO ¼ P K K þ P L L or $16 ¼ K þ 2L
where L and K stand for the quantity of labor and capital, respectively. Solving for K, we get
(c)
K ¼ TO
P K
P L
P K
L or K ¼ 16 2L
This means that the firm can buy 0L and 16K, or1L and 14K, or2L and 12K, or...8L and 0K. For each two
units of capital the firm gives up, it can purchase one additional unit of labor. Thus, the rate of substitution of L
for K in the marketplace is 2 (the absolute slope of the isocost) and remains constant.
P L refers to the wage that the firm must pay in order to hire labor or to purchase labor time for a specific period
of time. It can be expressed in dollars per labor-hour, dollars per worker-year, etc. Roughly speaking, P K is
given by the market rate of interest the firm must pay to borrow capital (for investmment purposes). For
example, the firm might have to pay 8% to borrow $100 for one year. In this case, P K ¼ $8. In our analysis,
we implicitly assumed that P L and P K remain constant, regardless of the quantity of labor and capital
demanded by the firm per unit of time. (Factor pricing is discussed in Chapter 13.)
6.17 Using the isoquants of Problem 6.12 and the isocost defined in Problem 6.16, determine the point at
which the producer is in equilibrium.
Fig. 6-18
The producer is in equilibrium at point N on isoquant II. Thus, in order to be in equilibrium, the producer
should spend $8 of its TO to purchase 8K and the remaining $8 to purchase 4L. At equilibrium, MRTS LK ¼ MP L /
MP K ¼ P L /P K ¼ 2. At point H, the MRTS LK exceeds the rate at which labor can be substituted for capital in the